Simmons, David orcid.org/0000-0002-9136-6635 (2016) On interpreting Patterson - : Sullivan measures of geometrically finite groups as Hausdorff and packing measures. Ergodic Theory and Dynamical Systems. pp. 2675-2686. ISSN 1469-4417
Abstract
We provide a new proof of a theorem whose proof was sketched by Sullivan ('82), namely that if the Poincar\'e exponent of a geometrically finite Kleinian group $G$ is strictly between its minimal and maximal cusp ranks, then the Patterson--Sullivan measure of $G$ is not proportional to the Hausdorff or packing measure of any gauge function. This disproves a conjecture of Stratmann ('97, '06).
Metadata
Authors/Creators: |
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Keywords: | math.DS |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 17 Dec 2015 09:05 |
Last Modified: | 06 Dec 2023 11:09 |
Published Version: | https://doi.org/10.1017/etds.2015.27 |
Status: | Published |
Refereed: | No |
Identification Number: | https://doi.org/10.1017/etds.2015.27 |
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